In casual conversation, a particle can sometimes be left unspoken when the surrounding words and context already make the noun's role clear. The noun itself stays in the sentence; only the particle is omitted.
What is actually omitted
Nothing changes form: the speaker simply leaves out a particle that the listener can easily supply. A pause after the noun may remain, but the pause is not a replacement particle. Omission is most natural when the verb strongly suggests the noun's role or the speakers already share the relevant context.
Common casual patterns
These short questions sound natural because the missing relationship is easy to recover.
In this familiar situation, the giving verb makes it easy to understand what is being given and who receives it. This degree of omission belongs to relaxed speech and depends heavily on context.
When the subject marker matters
Casual omission works when the noun's role is already predictable. By contrast, when a question asks the listener to identify the subject, が does important work and should remain.